In this section two representative models are presented to display
the distinguished characteristics of \(\gamma _g\)  or \(z\)  for the
determination of the phase diagram in many-body systems. One is the
\(D\) -dimensional free-fermion model, in which the quantum phase
transition is originated from the degeneracy of the ground-state
energy [1]}. The other is the Su-Schrieffer-Heeger (SSH)
model, in which the quantum phase transition happens with the
non-vanishing energy gap above the ground state [2]}. It is
obvious that these examples include two important cases of quantum
phase transition; one is the degeneracy of the ground-state energy,
whereas not for the other. Moreover the both models are exactly
solvable.
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